Applying Goodman, Gerber, Soderberg and Elliptical failure theories does not make it possible to determine the span of failure times (cycles to failure-$N_i$) of a mechanical element, and so in this paper a fatigue-life/Weibull method to predict the span of the $N_i$ values is formulated. The input’s method are: (1) the equivalent stress (${\sigma }_{eq}$) value given by the used failure theory; (2) the expected $N_{eq}$ value determined by the Basquin equation; and (3) the Weibull shape β and scale η parameters that are fitted directly from the applied principal stress ${\sigma }_1$ and ${\sigma }_2$ values. The efficiency of the proposed method is based on the following facts: (1) the β and η parameters completely reproduce the applied ${\sigma }_1$ and ${\sigma }_2$ values. (2) The method allows us to determine the reliability index R(t), that corresponds to any applied ${\sigma }_{1i}$ value or observed $N_i$ value. (3) The method can be applied to any mechanical element’s analysis where the corresponding ${\sigma }_1$ and ${\sigma }_2$, ${\sigma }_{eq}$ and $N_{eq}$ values are known. In the performed application, the ${\sigma }_1$ and ${\sigma }_2$ values were determined by finite element analysis (FEA) and from the static stress analysis. Results of both approaches are compared. The steps to determine the expected $N_i$ values by using the Weibull distribution are given.

In this paper, a Weibull probabilistic methodology is proposed with an approach to model vibration fatigue damage accumulation using two parameters: Weibull distribution and a nonlinear fatigue damage accumulation model. The damage is cumulated based on the application of a vibration stress profile and is used to determine both the Weibull $\beta$ and $\eta$ parameters, and the corresponding component reliability R(t). The vibration fatigue damage is analyzed to accumulate the damage as a stress function for a fatigue life exponent derived with the assistance of the acceleration’s force response. The steps to determine the Weibull $\beta$ and $\eta$ parameters are estimated based only on the principal vibration stresses ${\sigma }_1$ and ${\sigma }_2$ that allow the reproduction of the vibration fatigue damage. The method’s efficiency is based on the probabilistic approach by using the vibration fatigue damage as the Y_i vector that covers the arithmetic mean as well as the $\beta$ parameter. Finally, the procedure proposed is applied in a practical case where a mechanical component is used as a support for telecommunication connections and is submitted to vibration stress. The results show that using the damage accumulated as the Y_i vector to estimate the parameters allows for the analysis of dynamic and individual applications.

The paper’s content allowed us to determine the fatigue life of a component that is being subjected to a random vibration environment. Its estimation is performed in the frequency domain with loading frequencies being closer to the system’s natural frequency. From loads’ amplitude and their interaction effect, we derive a nonlinear damage model to cumulate the generated fatigue damage. The exponent value of 0.4 from the Manson–Halford curve damage model was replaced by a vibration bending stress relation that considers the effect and interaction of loads. The analysis is performed from a progressive accelerated vibration spectrum to predict the fatigue life estimation. From this accelerated scenario, the accelerated coefficients and cumulated damage are both determined. The proposed nonlinear model is based on the following facts: (1) vibration and bending stress ${\sigma }_{vb}$ values are obtained from the response acceleration of power spectral density (PSD) applied and (2) the model can be applied to any mechanical component analysis where the corresponding acceleration responses $A_{res}$ and the dynamic load factor ${\sigma }_{dynamic}$ values are known. The steps to determine the expected fatigue damage accumulation D by using the curve damage are given.

Since the designed bearing’s reliability of 90% was determined in a lab environment, it does not represent the actual used environment. In this paper, a new methodology to determine the actual reliability that corresponds to the use conditions is offered. This new method is based on the standard method used to select the ball bearing. The proposed method is based on the two parameters of Weibull distribution, where the shape (β) and scale (η) parameters are both determined from the Hertz contact stresses values, which are generated under the surface of the motionless outer race, and by the forces transmitted between the ball and the outer race. Therefore, the derived reliability is different from the 90% index offered by manufacturers.

In this paper a Weibull methodology to determine the probabilistic percentiles for the S-N curve of the A572 Gr. 50 steel is formulated. The given Weibull/S-N formulation is based on the true stress and true strain values, which are both determined from the stress-strain analysis. For the analysis, the Weibull β and η parameters are both determined directly from the maximum and minimum addressed stresses values. The S-N curve parameters are determined for 10³ and 10⁶ cycles. In the application, published experimental data for the CSA G40.21 Gr. 350W steel is used to derive the true stress and true strain parameters of the A572 Gr. 50 steel. Additionally, the application of the S-N curve, its probabilistic percentiles and the Weibull parameters that represent these percentiles are all determined step by step. Since the proposed method is flexible, then it can be applied to determine the probabilistic percentiles of any other material.

The service life assessment of previous fatigue stress has a fundamental role in estimating the reliability of products like fiber optical connectors, and should replicate use in severe environments in telecommunications systems. However, the vibration prediction models used in the literature present limitations in vibration life prediction. In this paper, we propose using the insertion loss fatigue life and including it in the Weibull distribution to determine the Weibull parameters ƞ and β to evaluate fiber optic connector reliability R(t) under environmental and mechanical testing stress. We analyzed the failure data of a standard telecommunication fiber optical connector under a program of service life stress testing against that of a fiber optical connector under only mechanical vibration stress testing. The fiber connectors were monitored during the vibration testing to review the transient change of the optical signal. Their results showed that the reliability of the fiber connectors submitted to the service life program was $R\left(t\right)=0.694$, while that of the fiber connectors submitted to mechanical vibration only was $R\left(t\right)=0.970$. In addition, the analysis showed that the service life testing consumed 70.2% of the product’s lifetime. We present in Numerical Validation the steps to determine the acceleration factors of the vibration test developed.